The entropy change of fuzzy numbers with arithmetic operations
The paper discusses some properties of the non-probabilistic entropy of fuzzy quantities as introduced by \textit{A. De Luca} and \textit{S. Termini} [Inform. and Control 20, 301-312 (1972; Zbl 0239.94028)]. The formulation of this entropy, more correctly, of a measure of fuzziness \(H\), is not correct for the authors' next considerations because of its dependence on the underlying universe \(X\), as far as it is not ensured that all discussed fuzzy sets are the fuzzy subsets of \(X\) (especially \(C\) in Theorem 4, \(D_1\) and \(D_2\) in Theorem 5, etc.). Also the relationship of the entropy functions \(h\) and \(H\) is not well clarified (in general, \(h\) may depend on \(x)\). The main results of the paper show that the entropy \(H\) has several properties of linearity on the class of triangular fuzzy numbers. Note that these properties hold for the large class of LR-fuzzy numbers as shown by \textit{A. Kolesárová} and \textit{D. Vivona} [Kybernetika 37, 127-145 (2001)].
non-probabilistic entropy of fuzzy quantities
scientific article; zbMATH DE number 1437006
scientific article